Direct Simulation of Thermoacoustic Instability in Gas Generators Using the CABARET Scheme

It is shown that the nondissipative CABARET scheme can be used to find the conditions for the occurrence of thermoacoustic instability (vibrational combustion) in the combustion chambers of gas turbine engines. The propagation of long waves in the gas-dynamic tract is described quite accurately by a system of quasi-linear equations of gas dynamics, averaged over the cross section. Numerical modeling of the dynamics of acoustic disturbances and their interaction with the combustion zone (in the presence of feedbacks) using nondissipative difference schemes (direct modeling) is a real alternative to the so-called low-order network models that replace the acoustic tract (by analogy with AC power grids) with a sequence of a four-pole or six-pole network. The advantages of direct modeling include the ease of accounting for geometric factors, nonlinear effects, and the possibility of using more realistic combustion models. As an example of using the direct method, a model problem of the excitation of sound vibrations in a tube in the presence of heat sources (Rijke tube) is solved. The results demonstrate the accuracy of the method in determining the growth rate of unstable modes, comparable to the accuracy of the results obtained using low-order network models.